I. Technical Field
This invention pertains to telecommunications, and particularly to the shaping of pulses which are utilized in the transmission of information in wireless telecommunications.
II. Related Art and Other Considerations
In a typical cellular radio system, wireless terminals (also known as mobile terminals, mobile stations, and mobile user equipment units (UEs)) communicate via base stations of a radio access network (RAN) to one or more core networks. The wireless terminals (WT) can be mobile stations such as mobile telephones (“cellular” telephones) and laptops with mobile termination, and thus can be, for example, portable, pocket, hand-held, computer-included, or car-mounted mobile devices which communicate voice and/or data with radio access network. The base station, e.g., a radio base station (RBS), is in some networks also called “NodeB” or “B node”. The base stations communicate over the air interface (e.g., radio frequencies) with the wireless terminals which are within range of the base stations.
There are various techniques for conditioning and transmitting a signal over a radio or wireless interface, e.g., between a base station and a wireless terminal. One technique is orthogonal frequency division multiplexing (OFDM). The OFDM spread-spectrum scheme is employed for many broadly used applications, including digital TV broadcasting in Australia, Japan and Europe; digital audio broadcasting in Europe; Asynchronous Digital Subscriber Line (ADSL) modems and wireless networking worldwide (IEEE 802.11a/g).
In an OFDM system, a very high rate data stream is divided into multiple parallel low rate data streams. Each smaller data stream is then mapped to an individual data sub-carrier and modulated using some flavor of PSK (Phase Shift Keying) or QAM (Quadrature Amplitude Modulation), i.e., BPSK, QPSK, 16-QAM, 64-QAM.
Transmitting a signal at a high modulation rate through a band-limited channel, whether processed by OFDM techniques or otherwise, can create intersymbol interference. As the modulation rate increases, the signal's bandwidth increases. When the signal's bandwidth becomes larger than the channel bandwidth, the channel starts to introduce distortion to the signal, which distortion is usually seen as intersymbol interference (ISI).
A pulse shaping process can be utilized to change the waveform of the transmitted communication signal. Pulse shaping serves to render a transmitted signal better suited to the communication channel over which it is to be transmitted, and does so by, e.g., limiting the effective bandwidth of the transmission. By filtering the transmitted pulses using a pulse shaping waveform, the intersymbol interference caused by the channel can be controlled.
The pulse shape thus has significance to signal quality. A Nyquist pulse is a pulse shape that goes through zero at integer multiples of the symbol rate away from its peak, thus ensuring that, when sampled at the optimum point, the signal exhibits no Intersymbol Interference from any symbols adjacent to the sampled symbol. The Fourier Transform of the Nyquist pulse shape defines a filtering function in the frequency domain that will produce a Nyquist pulse shape at its output from an impulse at its input. Since it is usual to have filters at both the transmitter and the receiver, the former for limiting the transmitted spectrum and the latter for limiting the receiver response to adjacent channel signals, it is often decided to split the filtering function defined by the Fourier Transform of a Nyquist pulse shape equally between the transmitter and the receiver, and to thus use a “root-Nyquist” filter in each. Since the combined frequency response of the transmitter and the receiver is the product of their individual frequency responses, the result of multiplying the two root-Nyquist filters is a filter with the Nyquist property.
Pulse shapes are known in the art which are limited in their spectral extent but unlimited in their time duration, and which have the root-Nyquist property. For example, a pulse whose Fourier Transform has a Root-Raised-Cosine shape has a square which is Raised-Cosine shaped, and this is a Nyquist filter for symbol rates which are equal to twice the −6 dB single-sided bandwidth, or equal to the −6 dB two-sided bandwidth. Such a filter shape is Nyquist because, if it is folded about its −6 dB point and the overlapping folded portions added, the result is unity across the bandwidth. Therefore, no in-band frequency component of a signal is altered by the filter. Such a filter is specified to be used in the IS136 US digital cellular TDMA system standard.
Pulse shapes are also known which are limited in their time duration but which are infinite in the frequency domain, and which have the Root-Nyquist property in both the time and frequency domains. For example the IOTA pulse (Isoptropic Orthogonal Transform Algorithm) has been proposed for pulse-shaping OFDM symbols. Improvements to the IOTA pulse are also disclosed in U.S. Pat. No. 7,103,106, which is incorporated by reference herein.
That a function can be its own Fourier Transform is also known from the Gaussian function. The Gaussian function is infinite in extent in both the time and frequency domains, but falls off rapidly in both, so that ultimate truncation does not have serious deleterious effects. Gaussian filtering is specified for the GSM digital cellular system's MSK transmissions, which are then known as GMSK. Unfortunately the Gaussian waveshape is not Nyquist; therefore GSM transmissions are generally received using an equalizer to cancel the resultant intersymbol-interference, even when the propagation path does not introduce intersymbol interference (ISI).